According to the inverse square law, what does (I1)(D1)^2 equal to?

The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. This principle can be expressed mathematically with the equation ( I \propto \frac{1}{D^2} ). When two different intensities (I1 and I2) are measured at two different distances (D1 and D2) from a source, the relationship can be set up as follows:

[

(I1)(D1^2) = (I2)(D2^2)

]

This equation indicates that the product of the intensity at distance D1 and the square of that distance equals the product of the intensity at distance D2 and the square of that distance. This relationship showcases how when you double the distance from a source, the intensity drops by a factor of four, emphasizing the inverse square relationship that governs the behavior of radiation in this context.

The other mathematical expressions do not adhere to the inverse square law. For example, addition or multiplication of the intensities and distances in the other options do not reflect the correct relationship as described by the inverse square law in physics. Therefore, the correct representation of the law is captured in the first option.